Surely someone who has problems with RAW files from Canon 5D Mk111, can arrange for a sample of a couple of raw files copied from a card reader direct to Winows Explorer or Finder in Mac, so they have been untouched by either Lightroom or Canon software. Post the samples via "yousendit(dot)com" or similar file transfer providers, which will enable interested users on this forum to test on their systems with Lightroom. It may isolate issues with particular Canon 5D Mk111 cameras creating partially corrupt files.
As a thought maybe certain Compact Flash and SD cards that work with earlier Canon Camera models are not able to efficiently handle the files from the new model.